There is no obvious semantic link between the noun _ilk_ “sort, kind” and the animal of the family Cervidae, so this substitution surprises at first and cast doubt on its status as a genuine eggcorn.
Occurrences of _X and his/her/their elk_ are, however, readily found in online writing, and some of them are clearly systematic and non-accidental: The writer for _Leadership Nigeria_ employs the expression no less than 5 times.
On Language Log, reporting on Nancy Friedman’s original Sarah Palin example, Ben Zimmer offers some thoughts on what may be going on here:
> There’s nothing in the comment to suggest that this substitution was the result of intentional wordplay, but it’s hard not to think that the slip was influenced by Palin’s well-documented love of hunting big game in Alaska like moose and caribou. […] And perhaps the commenter is from a part of the country where milk is pronounced as [mɛlk] (say, Pittsburgh, Utah, or Washington State), rendering ilk and elk homophonous, or nearly so. Add the fact that ilk is a low-frequency word that lingers in crystallized idiomatic usage (”of X’s ilk,” “X and his/her/its/their ilk”), and it’s clear to see that this is a prime candidate for eggcornization.
Meanwhile in the Eggcorn Forum, our regular contributor Kem Luther finds a particular affinity between Sarah Palin and the _ilk>elk_ eggcorn, thereby strengthening Ben Zimmer’s point of a Palin -> Alaska -> elk connection:
* _And it is Palin and her elk that are running everyone else out of the republican party._ (Reader comment on Talking Points Memo)
* _i would rather be in hell first, than have anything to do with Christians like Sarah Palin and her Elk._ (Castlebar.ie forum)
This is notwithstanding the fact that _Cervus canadensis_ is not specifically typical for Alaska. On the other hand, British English admits _elk_ for the animal called _moose_ in American English - compare with _Elch_ in German - and it should be noted that some of the cites are from British and Irish sources. (More on this topic in Bill Poser’s LL post.)
But to paraphrase commenter marie-lucie on Ben Zimmer’s article, if there is Artemis and her stag, why not Sarah Palin and her elk?
As the examples, show, however, the substitution is more than a Palin-specific nonce-eggcorn. It may still be questionable, used by writers who pronounce _ilk_ as [ɛlk] ans spell it phonetically; or it may reflect a genuine ideation of a cervid stand-in for the extension of the person who is the target of the speaker’s, or writer’s, finger-pointing.